Comparison of the Shapiro-Wilk and Kurtosis Tests for the Detection of Pulsed Sinusoidal Radio Frequency Interference

Normality tests have been shown to be powerful tools for detecting radio frequency interference (RFI) in microwave radiometer systems [1]-[4]. These tests are based on the fact that received fields produced by thermal noise are Gaussian (or “normal”) random variables; the presence of any RFI generally disrupts normality. Numerous statistical tests of the normality of a data sample have been described in the literature, but to date only the kurtosis test ([5]-[6]) has been demonstrated for microwave radiometer applications ([1]-[4]). The results of [1]-[4] show the kurtosis test to provide high sensitivity to low duty cycle pulsed as well as continuous sinusoidal RFI, but “blind spots” for which the algorithm is insensitive to RFI have also been shown. This report documents an examination of an alternate test for normality called the Shapiro-Wilk test, and compares its performance with that achieved by the kurtosis test for pulsed and continuous sinusoidal RFI. The Shapiro-Wilk test was first proposed in 1965 [7], and has been shown to be capable of detecting non-normality for a wide variety of statistical distributions, including those with Gaussian kurtosis values [8]. The discussion to follow largely parallels the analysis previously presented for the kurtosis test [3]. Note the results consider only pulsed and continuous sinusoidal ∗The Ohio State University, Department of Electrical and Computer Engineering and ElectroScience Laboratory, 1320 Kinnear Road, Columbus, OH 43210, USA. Email: [email protected]